Moreira, Helmar Nunes and Araujo, Ricardo Azevedo (2011): On the existence and the number of limit cycles in evolutionary games.

PDF
MPRA_paper_33895.pdf Download (453kB)  Preview 
Abstract
In this paper it is shown that an extended evolutionary system proposed by Hofbauer and Sigmund (1998) may be transformed into a Kukles system. Then a DulacCherkas function related to the Kukles system is derived, which allows us to determine the number of limit cycles or its nonexistence.
Item Type:  MPRA Paper 

Original Title:  On the existence and the number of limit cycles in evolutionary games 
Language:  English 
Keywords:  limit cycles, evolutionary game theory, Kukles system, DulacCherkas function 
Subjects:  C  Mathematical and Quantitative Methods > C0  General > C02  Mathematical Methods C  Mathematical and Quantitative Methods > C7  Game Theory and Bargaining Theory > C73  Stochastic and Dynamic Games ; Evolutionary Games ; Repeated Games 
Item ID:  33895 
Depositing User:  Ricardo Araujo 
Date Deposited:  05. Oct 2011 20:08 
Last Modified:  22. Oct 2015 16:39 
References:  Chang, W. and Smith, D. 1971. The existence and persistence of cycles in a nonlinear model: Kaldor’s 1940 model reexamined. Review of Economic Studies 38, 37 – 44. Cheng, K. 1981. Uniqueness of a Limit Cycle for PredatorPrey System. SIAM Journal of Mathematical Analysis and Applications 12, 115 – 126. Cherkas, L. 1978. Conditions for the equation to have a center. Differential Equations 14, 11331138. Cherkas, L., Grin, A. and Schneider,K. 2011. DulacCherkas functions for generalized Liénard systems. Electronic Journal of Qualitative theory of Differential Equations 35123. Dockner, E. and Feichtinger. On the optimality of Limit Cycles in Dynamic Economic Systems. Journal of Economics 53(1), 31 – 50. Feichtinger, G. 1987. Limit cycles in economic control models. Optimal Control: Lecture Notes in Control and Information Sciences 95, 4655. Feichtinger, G. 1992. Limit cycles in dynamic economic systems Annals of Operations Research 37(1), 313344. Feichtinger, G., Novak, A. and Wirl, F. 2002. Limit cycles in intertemporal adjustment models: Theory and applications. Journal of Economic Dynamics and Control 18(2), 353 – 380. Gasull, A. and Giacomini, H. 2006. Upper bounds for the number of limit cycles through linear differential equations. Pacific Journal of Mathematics 23, 6277 – 296. Goodwin, R. 1951. The Nonlinear Accelerator and the Persistence of Business Cycles. Econometrica 19, 1 – 17. Hofbauer,J. and Sigmund,K. 1998. Evolutionary Games and Population Dynamics. Cambridge University Press, Cambridge. Hofbauer, J. and So, J. 1990. Multiple Limit Cycles for PredatorPrey Model. Mathematical Biosciences 99, 71 – 75. Hofbauer, J. and So, J. 1994. Multiple Limit Cycles in three Dimensional LotkaVolterra Equations. Applied Mathematics Letters 7(6), 59 – 63. Sáez, E. and Szántó, I. 2008. Coexistence of Algebraic and Nonalgebraic Limit Cycles in Kukles Systems. Periodica Mathematica Hungarica, 56 (1), 137–142. Weibull, J. 1996. Evolutionary Game Theory. The MIT Press. Cambridge, Massachusetts. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/33895 